Boundary Integral Equations on Contours with Peaks: 196 (Operator Theory: Advances and Applications) - Tapa dura

Maz'ya, Vladimir; Soloviev, Alexander

9783034601702: Boundary Integral Equations on Contours with Peaks: 196 (Operator Theory: Advances and Applications)

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ISBN 10: 3034601700 ISBN 13: 9783034601702

Editorial: Birkh�user, 2009

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1 Lp -theory of boundary integral equations on a contour with peak.- 1.1 Introduction.- 1.2 Continuity of boundary integral operators.- 1.3 Dirichlet and Neumann problems for a domain with peak.- 1.4 Integral equations of the Dirichlet and Neumann problems.- 1.5 Direct method of integral equations of the Neumann and Dirichlet problems.- 2 Boundary integral equations in H�lder spaces on a contour with peak.- 2.1 Weighted H�lder spaces.- 2.2 Boundedness of integral operators.- 2.3 Dirichlet and Neumann problems in a strip.- 2.4 Boundary integral equations of the Dirichlet and Neumann problems in domains with outward peak.- 2.5 Boundary integral equations of the Dirichlet and Neumann problems in domains with inward peak.- 2.6 Integral equation of the first kind on a contour with peak.- 2.7 Appendices.- 3 Asymptotic formulae for solutions of boundary integral equations near peaks.- 3.1 Preliminary facts.- 3.2 The Dirichlet and Neumann problems for domains with peaks.- 3.3 Integral equations of the Dirichlet problem.- 3.4 Integral equations of the Neumann problem.- 3.5 Appendices.- 4 Integral equations of plane elasticity in domains with peak.- 4.1 Introduction.- 4.2 Boundary value problems of elasticity.- 4.3 Integral equations on a contour with inward peak.- 4.4 Integral equations on a contour with outward peak.- Bibliography.

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This book is a comprehensive exposition of the theory of boundary integral equations for single and double layer potentials on curves with exterior and interior cusps. Three chapters cover harmonic potentials, and the final chapter treats elastic potentials.

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An equation of the form ??(x)? K(x,y)?(y)d?(y)= f(x),x?X, (1) X is called a linear integral equation. Here (X,?)isaspacewith ?-?nite measure ? and ? is a complex parameter, K and f are given complex-valued functions. The function K is called the kernel and f is the right-hand side. The equation is of the ?rst kind if ? = 0 and of the second kind if ? = 0. Integral equations have attracted a lot of attention since 1877 when C. Neumann reduced the Dirichlet problem for the Laplace equation to an integral equation and solved the latter using the method of successive approximations. Pioneering results in application of integral equations in the theory of h- monic functions were obtained by H. Poincar� e, G. Robin, O. H� older, A.M. L- punov, V.A. Steklov, and I. Fredholm. Further development of the method of boundary integral equations is due to T. Carleman, G. Radon, G. Giraud, N.I. Muskhelishvili,S.G.Mikhlin,A.P.Calderon,A.Zygmundandothers. Aclassical application of integral equations for solving the Dirichlet and Neumann boundary value problems for the Laplace equation is as follows. Solutions of boundary value problemsaresoughtin the formof the doublelayerpotentialW? andofthe single layer potentialV?. In the case of the internal Dirichlet problem and the ext- nal Neumann problem, the densities of corresponding potentials obey the integral equation ???+W? = g (2) and ? ???+ V? = h (3) ?n respectively, where ?/?n is the derivative with respect to the outward normal to the contour.

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EditorialBirkh�user
A�o de publicaci�n2009
ISBN 10 3034601700
ISBN 13 9783034601702
Encuadernaci�nTapa dura
IdiomaIngl�s
N�mero de p�ginas360
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Boundary Integral Equations on Contours with Peaks

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Buch. Condici�n: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -An equation of the form (x) K(x,y) (y)d (y)= f(x),x X, (1) X is called a linear integral equation. Here (X, )isaspacewith - nite measure and is a complex parameter, K and f are given complex-valued functions. The function K is called the kernel and f is the right-hand side. The equation is of the rst kind if = 0 and of the second kind if = 0. Integral equations have attracted a lot of attention since 1877 when C. Neumann reduced the Dirichlet problem for the Laplace equation to an integral equation and solved the latter using the method of successive approximations. Pioneering results in application of integral equations in the theory of h- monic functions were obtained by H. Poincar e, G. Robin, O. H older, A.M. L- punov, V.A. Steklov, and I. Fredholm. Further development of the method of boundary integral equations is due to T. Carleman, G. Radon, G. Giraud, N.I. Muskhelishvili,S.G.Mikhlin,A.P.Calderon,A.Zygmundandothers. Aclassical application of integral equations for solving the Dirichlet and Neumann boundary value problems for the Laplace equation is as follows. Solutions of boundary value problemsaresoughtin the formof the doublelayerpotentialW andofthe single layer potentialV . In the case of the internal Dirichlet problem and the ext- nal Neumann problem, the densities of corresponding potentials obey the integral equation +W = g (2) and + V = h (3) n respectively, where / n is the derivative with respect to the outward normal to the contour. 344 pp. Englisch. N� de ref. del art�culo: 9783034601702

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Boundary Integral Equations on Contours with Peaks

Vladimir Maz'ya

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ISBN 10: 3034601700 ISBN 13: 9783034601702

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Buch. Condici�n: Neu. Druck auf Anfrage Neuware - Printed after ordering - An equation of the form (x) K(x,y) (y)d (y)= f(x),x X, (1) X is called a linear integral equation. Here (X, )isaspacewith - nite measure and is a complex parameter, K and f are given complex-valued functions. The function K is called the kernel and f is the right-hand side. The equation is of the rst kind if = 0 and of the second kind if = 0. Integral equations have attracted a lot of attention since 1877 when C. Neumann reduced the Dirichlet problem for the Laplace equation to an integral equation and solved the latter using the method of successive approximations. Pioneering results in application of integral equations in the theory of h- monic functions were obtained by H. Poincar e, G. Robin, O. H older, A.M. L- punov, V.A. Steklov, and I. Fredholm. Further development of the method of boundary integral equations is due to T. Carleman, G. Radon, G. Giraud, N.I. Muskhelishvili,S.G.Mikhlin,A.P.Calderon,A.Zygmundandothers. Aclassical application of integral equations for solving the Dirichlet and Neumann boundary value problems for the Laplace equation is as follows. Solutions of boundary value problemsaresoughtin the formof the doublelayerpotentialW andofthe single layer potentialV . In the case of the internal Dirichlet problem and the ext- nal Neumann problem, the densities of corresponding potentials obey the integral equation +W = g (2) and + V = h (3) n respectively, where / n is the derivative with respect to the outward normal to the contour. N� de ref. del art�culo: 9783034601702

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Boundary Integral Equations on Contours with Peaks (Operator Theory: Advances and Applications, 196)

Maz'ya, Vladimir; Soloviev, Alexander

Publicado por Birkh�user, 2009

ISBN 10: 3034601700 ISBN 13: 9783034601702

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Condici�n: New. In English. N� de ref. del art�culo: ria9783034601702_new

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Boundary Integral Equations on Contours with Peaks

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